At `27^(@)C` a gas contains 10 molecules travelling with a speed of 4 `ms^(-1)`, 20 molecules travelling with a speed of 5 m `s^(-1)` and 40 molecules travelling with a speed of 8 m `s^(-1)`. Calculate the average speed, root mean square speed and most probable speed of the gas at `27^(@)C`.

Explanation

Average speed `(overset(bar)(c )=(sumn_(i)v_(i))/(sumn_(i))=(10xx4+20xx5+40xx8)/(10+20+40)=(460)70)`
`=6.56 m s^(-1)`
Root mean square speed (c )`=sqrt((sumn_(i)v_(i))/(sumn_(i)))=sqrt((10xx4^(2)+20xx5^(2)+40xx82)/(10+20+40))`
`=sqrt((160+500+2560)/(70))=6.678 m s^(-1)`
Most probable speed `(c^(**))=0.816xxc=0.816xx6.78 m s^(-1)=5.53 m s^(-1)`.